External validation of a prediction model for estimating fat mass in children and adolescents in 19 countries: individual participant data meta-analysis.

OBJECTIVE: To evaluate the performance of a UK based prediction model for estimating fat-free mass (and indirectly fat mass) in children and adolescents in non-UK settings.
DESIGN: Individual participant data meta-analysis.
SETTING: 19 countries. PARTICIPANTS: 5693 children and adolescents (49.7% boys) aged 4 to 15 years with complete data on the predictors included in the UK based model (weight, height, age, sex, and ethnicity) and on the independently assessed outcome measure (fat-free mass determined by deuterium dilution assessment). MAIN OUTCOME MEASURES: The outcome of the UK based prediction model was natural log transformed fat-free mass (lnFFM). Predictive performance statistics of R2, calibration slope, calibration-in-the-large, and root mean square error were assessed in each of the 19 countries and then pooled through random effects meta-analysis. Calibration plots were also derived for each country, including flexible calibration curves.
RESULTS: The model showed good predictive ability in non-UK populations of children and adolescents, providing R2 values of >75% in all countries and >90% in 11 of the 19 countries, and with good calibration (ie, agreement) of observed and predicted values. Root mean square error values (on fat-free mass scale) were <4 kg in 17 of the 19 settings. Pooled values (95% confidence intervals) of R2, calibration slope, and calibration-in-the-large were 88.7% (85.9% to 91.4%), 0.98 (0.97 to 1.00), and 0.01 (-0.02 to 0.04), respectively. Heterogeneity was evident in the R2 and calibration-in-the-large values across settings, but not in the calibration slope. Model performance did not vary markedly between boys and girls, age, ethnicity, and national income groups. To further improve the accuracy of the predictions, the model equation was recalibrated for the intercept in each setting so that country specific equations are available for future use.
CONCLUSION: The UK based prediction model, which is based on readily available measures, provides predictions of childhood fat-free mass, and hence fat mass, in a range of non-UK settings that explain a large proportion of the variability in observed fat-free mass, and exhibit good calibration performance, especially after recalibration of the intercept for each population. The model demonstrates good generalisability in both low-middle income and high income populations of healthy children and adolescents aged 4-15 years. © Author(s) (or their employer(s)) 2019. Re-use permitted under CC BY-NC. No commercial re-use. See rights and permissions. Published by BMJ.

Introduction

The high global prevalence of obesity in childhood poses a major global public health challenge. The World Health Organization recently estimated that about 18% of children and adolescents aged 5-19 years worldwide (>340 million individuals) are affected by overweight or obesity.1 However, the most widely used marker of high childhood adiposity, body mass index (BMI), has serious limitations.2 3 4 BMI is poorly correlated with fat mass in childhood and, crucially, as a weight-for-height index, BMI is unable to discriminate between fat mass and fat-free mass, which can both vary markedly in individuals with a given BMI.3 This is important, as fat mass in children has been shown to be more strongly associated with long term risk of type 2 diabetes than markers of body fatness based on overall weight (of which BMI is such a marker).5 The availability of simple, accurate methods for assessment of fat mass could represent an important advance in the assessment of adiposity over the use of BMI.4 6 In vivo techniques for the assessment of fat mass do exist, such as bioelectrical impedance analysis, dual energy x ray absorptiometry, and magnetic resonance imaging (MRI), but may lack accuracy,4 7 8 and, in the case of dual energy x ray absorptiometry and MRI are inappropriate for general use. An alternative accurate method for assessment of fat mass, which has been developed and validated within the UK population of children and adolescents,6 9 is based on the prediction of fat-free mass (and indirectly fat mass, as fat mass=weight−fat-free mass) using simple assessments of height, weight, sex, age, and ethnicity. Ethnicity was also included as a predictor within the developed model to allow for established differences in body fatness in children between ethnicities.10 11 12 To maximise the accuracy of the predictions obtained from this approach, the model was developed using data on fat mass in children obtained from the deuterium dilution approach, a reference standard method of adiposity assessment, which provides accurate, safe, and minimally invasive measurements of total body water (and fat-free mass) with an error of less than 1%.13 14 The developed model was also shown to predict fat mass levels as accurately as dual energy x ray absorptiometry and bioelectrical impedance analysis in UK children.9 However, the predictive performance of the model has not so far been examined in children and adolescents outside the UK.15 We therefore performed an external validation of the UK based fat mass prediction model to assess its predictive performance in a wide range of non-UK populations of children and adolescents aged 4-15 years with comparable fat mass assessment from the reference standard deuterium dilution method.

Methods

Data sources and study population

We carried out a Medline literature search through PubMed to identify all published studies that used the deuterium dilution method13 14 to assess fat-free mass and fat mass in at least 100 healthy children or adolescents aged between 4 and 15 years and also included measurements of weight and height and basic personal information on age and sex (search dates: May 2020, search terms: “deuterium dilution”, “study”, “children” or “adolescents”). Twenty four relevant studies were identified; study authors were contacted and invited to contribute data to this investigation. Fourteen agreed to participate, four were unable to participate owing to data sharing restrictions, and the remaining six did not respond. Study collaborators provided data from a further four studies (of which, one contained unpublished deuterium dilution data16 and two were small17 18). Further information is available in the Preferred Reporting Items for Systematic Reviews and Meta-analyses individual participant data (PRISMA-IPD) flow diagram (see supplementary file). Each of the 18 studies provided data on weight, height, age, sex, ethnicity, and deuterium dilution assessed total body water, fat mass, and fat-free mass. The earliest study was conducted in 1981-8219 and the latest in 2017-1920; most studies (83%) were carried out from 2000 (see supplementary table 1). In total, 5715 generally healthy children and adolescents aged 4-15 years were included from 18 studies spanning 19 countries: Australia,17 Austria,19 Bangladesh,21 Brazil,22 China,23 Mexico,24 25 Namibia,20 Nepal,26 the Netherlands,27 New Zealand,10 the Philippines,23 Peru,18 Poland,16 Russia,23 South Africa,20 23 Spain,28 Sri Lanka,29 Tunisia,30 and the US31 32 (see supplementary table 1). Although five of these countries (Peru n=56, Spain n=92, China n=95, Philippines n=80, and Australia n=42) had smaller participant numbers than anticipated,17 18 23 28 the data were included to avoid data wastage.

Outcome and predictor assessment

The outcome was natural log transformed fat-free mass (lnFFM), ascertained using the deuterium dilution reference method,13 14 which was also used as the outcome for the previously developed UK based prediction model.6 Five individuals with missing information on the outcome (lnFFM), one individual with an implausible weight value, and 16 individuals with implausible fat-free mass values (ie, fat-free mass greater than weight) were excluded. No other data were missing on the predictors of weight, height, age, sex, or ethnicity (classified as either white, black, South Asian, other Asian, or other). After these exclusions, 5693 children and adolescents aged 4-15 years were included in analyses.

Statistical analysis

All statistical analyses were conducted in Stata (version 17). We followed the Transparent Reporting of a multivariable model for Individual Prognosis Or Diagnosis (TRIPOD) guideline for the reporting of studies validating a multivariable prediction model.15

Evaluation of overall performance of UK based prediction model equation

We applied the UK based model equation6 (fig 1) to all children and adolescents within this external validation dataset to obtain a prediction of lnFFM from weight, height, age, sex, and ethnicity.

Fig 1

Recalibrated country specific model equations for prediction of natural log transformed fat-free mass in children and adolescents. Country specific constant term for UK obtained from equation provided in Hudda et al6

The predictive performance of the model equation was assessed within each country by comparing the deuterium dilution assessed lnFFM value with the predicted lnFFM value obtained from the UK based model. Model performance was assessed by examining established predictive performance measures of:

R2—the percentage of variance in deuterium dilution observed lnFFM explained by predicted lnFFM estimated by the UK based prediction model.

Root mean square error—the average difference between predicted lnFFM from the UK based model and the deuterium dilution observed lnFFM. Root mean square error indicates the absolute fit of the model to the data (ie, how close the model’s predicted values of lnFFM are to the deuterium dilution observed values of lnFFM).

Model calibration—assessed collectively by means of three measures: slope, calibration-in-the-large, and calibration plot.

Slope—obtained from the model regressing deuterium dilution observed values of lnFFM on model predicted values of lnFFM. The calibration slope reports on the accuracy of the predictions across the range of lnFFM values by evaluating the spread of the predicted values, and the slope has a target value of 1. A slope <1 suggests that predicted values are too high for children and adolescents with low observed values and too low for those with high observed values. A slope >1 suggests the opposite.

Calibration-in-the-large—intercept term obtained from a linear regression model of deuterium dilution observed values of lnFFM on model predicted values of lnFFM, where the slope is constrained to be the ideal of 1 (with a calibration-in-the-large of 0 being ideal). Calibration-in-the-large measures the overall agreement between average model predicted values of lnFFM and average deuterium dilution observed values of lnFFM (ie, it tells you about the systematic bias of predicted lnFFM obtained from the model when compared with the deuterium dilution observed values of lnFFM).

Calibration plot—graph of deuterium dilution observed lnFFM plotted against model predicted values of lnFFM with a local regression (loess) smoother fitted across all individuals to produce a flexible calibration curve (created using pmcalplot on Stata).

To summarise results across all countries, we pooled the country specific performance measures of R2, calibration slope, and calibration-in-the-large through a random effects meta-analysis to obtain an estimate of average performance and between country heterogeneity. The random effects meta-analysis model was fitted using the restricted maximum likelihood method33 using the Hartung-Knapp34 approach to adjust the standard error of the pooled performance measures. Heterogeneity was summarised for each of the performance measures of R2, calibration slope, and calibration-in-the-large using the estimate of between study variance (τ2) and a 95% prediction interval, which provides a range of values that the performance measure would be expected to fall within for a new individual setting.35 For the random effects meta-analysis, the variance and confidence interval for R2 was estimated using the Wald-type method outlined elsewhere,36 and 95% prediction intervals were capped at the maximum values of 100%. The model performance was also assessed within subgroups of sex, three year age groups (4-6, 7-9, 10-12, and 13-15 years), and ethnic origin. Additionally, the model performance was assessed separately in low-middle income and high income populations of children and adolescents, categorised using the World Bank income classification.37 The country specific classifications were obtained for the year of study commencement such that Australia, Austria, the Netherlands, New Zealand, Spain, the US, and Poland were classified as high income and the remaining 12 countries were classified as low-middle income.

Although the primary results focus on the model performance measures assessed comparing deuterium dilution observed values of lnFFM with model predicted lnFFM, as the UK based model was developed to predict fat-free mass on the log scale, root mean square error and calibration plots are also presented on the fat-free mass scale to improve the interpretability of the results.

Country specific recalibration of UK based prediction model equation

When systematic error in the UK based model’s prediction of lnFFM was observed across countries, we recalibrated the intercept term of the UK based equation to provide updated country specific equations. Within each country, we first estimated the linear predictor portion of the UK based model for all individuals before fitting a linear regression model with deuterium dilution observed values of lnFFM as the dependent variable and the linear predictor as the independent variable. The slope of this model was constrained to be 1, and the constant term from the model was used as the updated intercept term for that country. We re-examined the performance of the country specific recalibrated equations to assess the predictive performance of the updated model equations.

Patient and public involvement

For this external validation study based on secondary data analysis, no patients were directly involved in setting the research question, outcome measures, study design, or implementation. However, previous focus groups including members of the public had indicated the need to develop and validate new methods for body fatness assessment in children, which informed the development of this work. No patients were involved in the interpretation or writing up of results.

Results

Table 1 summarises the key characteristics of the 5693 children and adolescents included in the analysis, by country. The median age was 10.8 years—slightly higher than in the development population6 (median age 9.6 years). All studies included both boys and girls, except for one study that included only boys.19 Average levels of deuterium dilution assessed fat mass and fat-free mass were, as expected, higher in studies of older children, who were also generally taller and heavier than younger children (table 1). Median fat mass in this validation dataset (8.5 kg) was similar to that of the development population6 (8.4 kg), although fat-free mass was higher in this external validation dataset (27.8 kg) than in the development population (24.8 kg).6 The representation of different ethnic groups varied across the settings, with 15 countries including data from a single ethnic group (table 1).

Table 1

Basic summary statistics of the analysis population, by country. Values are median (25th to 75th centile) unless stated otherwise

Region and country (No of participants)	Age (years)	Height (m)	Weight (kg)	DD fat mass (kg)*	DD fat-free mass (kg)*	No (%) boys		Ethnic group (No, %)
								White	Black	South Asian	Other Asian		Other
North America
Mexico (n=330)	8.4 (7.4-9.9)	1.30 (1.25-1.40)	31.6 (24.6-40.8)	7.6 (5.2-12.4)	22.7 (19.6-28.4)	170 (51.5)		0 (0)	0 (0)	0 (0)		0 (0)	330 (100)
US (n=1810)	10.6 (8.3-13.0)	1.44 (1.30-1.58)	39.2 (28.2-53.6)	9.1 (5.7-15.0)	28.5 (21.3-38.8)	867 (47.9)		571 (32)	457 (25)	2 (0.1)		283 (16)	497 (27)
South America
Brazil (n=450)	13.3 (13.1-13.6)	1.58 (1.52-1.63)	49.5 (42.5-56.3)	10.1 (6.6-15.2)	38.1 (34.0-43.4)	236 (52.4)		0 (0)	0 (0)	0 (0)		0 (0)	450 (100)
Peru (n=56)	11.0 (8.5-13.5)	1.46 (1.32-1.55)	40.2 (32.4-50.6)	9.4 (5.8-14.6)	30.9 (23.9-35.5)	25 (44.6)		0 (0)	0 (0)	0 (0)		0 (0)	56 (100)
Europe
Austria (n=107)	12.0 (11.1-13.6)	1.49 (1.42-1.60)	40.1 (34.0-48.0)	5.5 (4.2-8.5)	33.2 (28.5-40.6)	107 (100.0)		107 (100)	0 (0)	0 (0)		0 (0)	0 (0)
Netherlands (n=716)	13.5 (12.8-14.1)	1.62 (1.57-1.68)	51.3 (44.9-58.9)	11.9 (8.8-16.9)	38.6 (34.0-43.6)	342 (47.8)		716 (100)	0 (0)	0 (0)		0 (0)	0 (0)
Poland (n=174)	7.3 (6.1-8.7)	1.25 (1.18-1.34)	24.6 (21.0-28.0)	4.3 (3.3-5.8)	20.0 (17.5-22.8)	81 (46.6)		174 (100)	0 (0)	0 (0)		0 (0)	0 (0)
Russia (n=197)	10.8 (8.9-13.7)	1.47 (1.34-1.62)	37.9 (28.8-51.5)	11.3 (8.3-17.3)	25.8 (20.0-33.1)	97 (49.2)		0 (0)	0 (0)	0 (0)		0 (0)	197 (100)
Spain (n=92)	14.0 (13.0-15.2)	1.61 (1.55-1.68)	55.8 (48.1-63.0)	13.7 (8.8-17.9)	42.7 (37.0-49.2)	46 (50.0)		89 (97)	2 (2)	0 (0)		0 (0)	1 (1)
North Africa
Tunisia (n=155)	9.0 (8.0-10.0)	1.38 (1.31-1.44)	32.0 (27.0-36.0)	8.0 (6.4-11.1)	23.1 (20.2-27.0)	80 (51.6)		0 (0)	0 (0)	0 (0)		0 (0)	155 (100)
Sub-Saharan Africa
Namibia (n=151)	10.0 (9.0-11.0)	1.38 (1.33-1.46)	33.3 (27.2-43.4)	8.6 (6.1-14.5)	23.6 (20.6-28.1)	66 (43.7)		0 (0)	114 (76)	0 (0)		0 (0)	37 (25)
South Africa (n=411)	8.0 (7.0-8.8)	1.24 (1.17-1.31)	23.7 (20.4-28.3)	5.5 (4.4-7.6)	17.6 (15.3-21.2)	175 (42.6)		0 (0)	411 (100)	0 (0)		0 (0)	0 (0)
South Asia
Bangladesh (n=187)	5.1 (5.0-7.1)	1.10 (1.02-1.17)	15.8 (14.1-18.4)	2.0 (1.4-2.8)	13.6 (12.2-16.2)	93 (49.7)		0 (0)	0 (0)	187 (100)		0 (0)	0 (0)
Nepal (n=100)	8.6 (8.3-9.0)	1.23 (1.16-1.29)	21.8 (18.0-25.8)	4.2 (3.3-5.8)	17.6 (14.6-20.2)	49 (49.0)		0 (0)	0 (0)	100 (100)		0 (0)	0 (0)
Sri Lanka (n=288)	10.0 (7.6-12.2)	1.37 (1.24-1.49)	31.5 (23.0-41.1)	9.1 (5.2-15.3)	21.5 (16.2-27.1)	162 (56.3)		0 (0)	0 (0)	288 (100)		0 (0)	0 (0)
East Asia
China (n=95)	10.0 (9.4-10.6)	1.38 (1.33-1.43)	32.2 (27.4-37.0)	6.2 (3.9-8.7)	25.6 (22.8-28.2)	48 (50.5)		0 (0)	0 (0)	0 (0)		95 (100)	0 (0)
Philippines (n=80)	15.4 (15.1-15.7)	1.57 (1.52-1.64)	48.9 (43.4-54.5)	13.8 (9.5-17.2)	34.9 (31.3-40.8)	32 (40.0)		0 (0)	0 (0)	0 (0)		80 (100)	0 (0)
Australasia
Australia (n=42)	8.2 (7.0-10.9)	1.33 (1.19-1.43)	27.2 (23.1-37.1)	6.6 (4.2-11.0)	21.9 (16.7-27.5)	27 (64.3)		0 (0)	0 (0)	42 (100)		0 (0)	0 (0)
New Zealand (n=252)	10.1 (7.4-12.4)	1.42 (1.27-1.54)	36.5 (28.6-50.0)	9.6 (6.3-15.6)	27.2 (21.7-37.1)	124 (49.2)		82 (33)	0 (0)	0 (0)		0 (0)	170 (67)

DD=deuterium dilution.

Assessment of UK based model performance in non-UK settings

The UK based model equation, when applied to the external validation data, produced high R2 values >75% in all countries and >90% in 11 of the 19 countries (table 2). When the country specific R2 values were pooled through random effects meta-analysis, the overall pooled R2 value was 88.66% (95% confidence interval 85.91% to 91.41%) (fig 2). The R2 values showed some evidence of between country heterogeneity (τ2=28.62), and the 95% prediction interval for the R2 value (ie, the expected range of R2 values that would be expected from applying the model to a previously unstudied population of children and adolescents) was 77.04% to 100.00%. Root mean square error values were generally low (≤0.11 in all countries except for Russia and Sri Lanka; table 2). The model demonstrated high levels of calibration in terms of the slope in each of the countries. The observed calibration slope estimates ranged between 0.91 in Spain and 1.05 in Australia and South Africa (table 2), with the country specific 95% confidence intervals around the respective slope term containing the ideal value of 1 in 15 of the 19 countries (table 2). The pooled calibration slope was 0.98 (95% confidence interval 0.97 to 1.00; fig 2), with no evidence of between country heterogeneity in the calibration slopes (τ2=0), and a 95% prediction interval of 0.92 to 1.05 for the calibration slope expected to be observed in a new country. Although the country specific calibration-in-the-large values were close to the ideal value of 0 for most countries, ranging from −0.12 in Russia to 0.10 in Bangladesh, the associated 95% confidence intervals failed to contain the ideal value of 0 in any of the settings (table 2). When pooled through random effects meta-analysis, the overall pooled calibration-in-the-large value was almost equal to the ideal value of 0 (0.01, 95% confidence interval −0.02 to 0.04; fig 2). Some heterogeneity was evident in the calibration-in-the-large values (τ2=0.0031), with a 95% prediction interval of −0.11 to 0.13 that would likely be observed in a new country. Graphically, the calibration plots also demonstrated the good levels of calibration across the range of lnFFM values within each of the countries (fig 3 and fig 4), including at the lower and upper ends of the distribution of lnFFM, with the flexible calibration curve close to the ideal 45 degree line of perfect calibration. However, the graphs further showed evidence of some systematic error in the prediction of lnFFM across settings (fig 3 and fig 4).

Table 2

External validation predictive performance statistics based on natural log transformed fat-free mass, by country

Region and country	No	R2 (%) (95% CI)	Calibration slope (95% CI)	Calibration-in-the-large (95% CI)	RMSE
North America
Mexico	330	92.95 (91.49 to 94.42)	1.01 (0.98 to 1.04)	0.05 (0.04 to 0.05)	0.08
US	1810	93.32 (92.72 to 93.91)	1.00 (0.99 to 1.01)	0.02 (0.01 to 0.02)	0.10
South America
Brazil	450	76.69 (72.92 to 80.46)	0.96 (0.91 to 1.01)	0.05 (0.04 to 0.06)	0.10
Peru	56	92.29 (88.41 to 96.17)	0.94 (0.87 to 1.01)	0.04 (0.02 to 0.06)	0.09
Europe
Austria	107	91.47 (88.37 to 94.56)	0.96 (0.90 to 1.02)	0.06 (0.05 to 0.07)	0.09
Netherlands	716	81.53 (79.09 to 83.97)	1.00 (0.97 to 1.04)	−0.03 (−0.03 to −0.02)	0.09
Poland	174	93.28 (91.36 to 95.21)	0.96 (0.92 to 0.99)	0.04 (0.03 to 0.05)	0.07
Russia	197	91.30 (88.98 to 93.62)	0.93 (0.89 to 0.97)	−0.12 (−0.13 to −0.10)	0.15
Spain	92	80.85 (73.82 to 87.89)	0.91 (0.82 to 1.00)	0.03 (0.01 to 0.05)	0.10
North Africa
Tunisia	155	80.98 (75.59 to 86.37)	1.02 (0.94 to 1.10)	−0.02 (−0.03 to −0.01)	0.08
Sub-Saharan Africa
Namibia	151	90.14 (87.16 to 93.13)	0.93 (0.88 to 0.98)	−0.06 (−0.07 to −0.05)	0.09
South Africa	411	91.95 (90.46 to 93.44)	1.05 (1.02 to 1.08)	−0.05 (−0.05 to −0.04)	0.08
South Asia
Bangladesh	187	89.50 (86.65 to 92.35)	0.99 (0.94 to 1.04)	0.10 (0.09 to 0.10)	0.11
Nepal	100	91.66 (88.53 to 94.79)	0.99 (0.93 to 1.04)	0.06 (0.05 to 0.07)	0.08
Sri Lanka	288	83.11 (79.56 to 86.67)	0.99 (0.94 to 1.04)	−0.06 (−0.07 to −0.04)	0.16
East Asia
China	95	85.10 (79.57 to 90.63)	0.98 (0.90 to 1.07)	0.08 (0.07 to 0.10)	0.11
Philippines	80	81.03 (73.55 to 88.51)	1.04 (0.93 to 1.15)	−0.05 (−0.07 to −0.03)	0.09
Australasia
Australia	42	96.64 (94.65 to 98.64)	1.05 (0.98 to 1.11)	0.03 (0.01 to 0.05)	0.07
New Zealand	252	92.96 (91.29 to 94.64)	0.98 (0.94 to 1.01)	0.03 (0.02 to 0.04)	0.10

RMSE=root mean square error.

Fig 2

Assessment of R2 values, calibration slope, and calibration-in-the-large based on natural log transformed fat-free mass, by country and overall. Overall estimates from random effect restricted maximum likelihood model with Hartung-Knapp standard errors. Purple line around the overall diamond indicates the 95% prediction intervals. Upper limit of the prediction interval for R2 capped at 100%

Fig 3

Calibration assessment of the model based on natural log transformed fat-free mass (lnFFM) in the Americas and European countries. Solid black line represents line of equality. Dashed line is a loess smoother through the individual data points. Histogram is the distribution of predicted ln(FFM). Slope=calibration slope; CITL=calibration-in-the-large

Fig 4

Calibration assessment of the model based on natural log transformed fat-free mass (lnFFM) in African, Asian, and Australasian countries. Solid black line represents line of equality. Dashed line is a loess smoother through the individual data points. Histogram is the distribution of predicted ln(FFM). Slope=calibration slope; CITL=calibration-in-the-large

The generally high model performance was maintained when assessed across subgroups of sex (see supplementary figure 1), three year age groups (see supplementary figure 2), ethnic groups (see supplementary figure 3), and national income level (table 3). The model showed low levels of heterogeneity in the performance statistics across the three year age groups (see supplementary figure 4) and ethnic groups (see supplementary figure 5).

Table 3

External validation predictive performance statistics based on natural log transformed fat-free mass, by World Bank income classifications*

Performance statistics	Low-middle income group† (n=2473)	High income group‡ (n=3193)
R2 (%) (95% CI)	92.19 (91.60 to 92.78)	93.64 (93.21 to 94.07)
Calibration slope (95% CI)	0.98 (0.97 to 0.99)	0.97 (0.97 to 0.98)
Calibration-in-the-large (95% CI)	−0.00 (−0.01 to 0.00)	0.01 (0.01 to 0.01)
Root mean square error	0.11	0.10

Ascertained for initial calendar year the study began.

Comprises low, lower middle, and upper middle income groups. Includes Bangladesh, Brazil, China, Mexico, Namibia, Nepal, Peru, the Philippines, Russia, South Africa, Sri Lanka, and Tunisia.

Includes Australia, Austria, the Netherlands, New Zealand, Spain, US, and Poland.

On the fat-free mass scale, the country specific root mean square error values ranged between 1.32 kg and 4.83 kg, with a root mean square error value of <4 kg in 17 of the 19 countries (see supplementary table 2). Calibration plots showed good levels of agreement between deuterium dilution observed fat-free mass and model predicted fat-free mass within each of the countries, including at the lower and upper ends of the distribution of fat-free mass, with the flexible calibration curve close to the ideal 45 degree line of perfect calibration (see supplementary figures 6a and 6b).

As a result of the observed systematic error in the UK based model’s prediction of lnFFM, the equation was recalibrated for the intercept term to provide updated country specific equations (fig 1) and calibration plots (see supplementary figures 7a and 7b). After recalibration, the calibration-in-the-large and root mean square error values were closer to the ideal values of 0 in all settings, with all of the country specific 95% confidence intervals for the calibration-in-the-large now containing the ideal value (see supplementary table 3).

Discussion

Principal findings

We externally validated the predictive performance of a recently proposed model using weight, height, age, sex, and ethnicity to estimate lnFFM, developed and validated within a UK population of children and adolescents, in 19 other countries from several regions of the world. The developed model equation generally showed good predictive ability in these new settings, with good calibration of observed and predicted values, demonstrating the generalisability of the model in populations of children and adolescents outside the UK. The model equation produced high R2 values >80% in all settings, with root mean square error values (expressed in terms of fat-free mass for interpretability) <4 kg in most of the settings. The root mean square error of 0.1 for lnFFM indicates an error of 10% on predicted fat-free mass values, which takes into account that the absolute error in any individual child or adolescent will depend on the magnitude of his or her fat-free mass. Notably, the predictive performance was consistently high among both low-middle income and high income countries. Although the calibration slope statistics were close to the ideal value of 1 for all countries, the calibration-in-the-large values suggested a small systematic error in the prediction of lnFFM across settings. Therefore, the model equation was recalibrated for the intercept term to provide updated country specific prediction equations. After recalibration, the model performance showed improvement in the calibration-in-the-large and root mean square error values in all settings as expected.

Comparison with other studies

A small number of previous studies have developed models to estimate body fatness in populations of children and adolescents outside the UK,38 39 40 41 42 43 producing R2 values >80% comparable with those observed in the present study. However, direct comparisons of the performance of those models with the model being validated in this study are difficult for several reasons. Firstly, while those models also produced high R2 values >80%, their outcomes (fat mass percentage) are different from the outcome of the current model (absolute fat-free mass values). Although fat mass needs to be standardised for height before interpretation or comparisons between individuals (typically expressed as a fat mass index or as fat mass percentage), the use of absolute values (of either fat mass or fat-free mass) as the outcome of the prediction model produces more accurate and precise predictions than estimating fat mass percentage, which is derived from fat mass and weight and is more variable than the absolute values. Furthermore, as discussed previously,6 we chose to estimate absolute fat mass values indirectly (by predicting fat-free mass from the model and subtracting estimates from weight to obtain predicted fat mass) rather than directly (using fat mass as the outcome of the model), as the variability in fat-free mass with height (one of the strongest predictors of body composition) was more homogeneous than for fat mass and thus the indirect approach resulted in more precise fat mass predictions. We believe this modelling decision was one of the main reasons for the high predictive performance observed. Secondly, neither the calibration slopes nor the calibration-in-the-large values were assessed for these models. Thirdly, these models largely used dual energy x ray absorptiometry as the reference method for assessing body fatness (ie, as the outcome for model development). Estimation of fat mass using dual energy x ray absorptiometry is, however, prone to low levels of accuracy,4 7 8 44 45 which varies considerably by body shape, sex,8 44 and different dual energy x ray absorptiometry devices and software used. Finally, most models used additional measurements, including skinfold thickness, waist circumference, or bioelectrical impedance to estimate fat mass, rather than being based on readily available anthropometric and demographic predictors.39 40 41 42 43 One such study, which used the same data on Tunisian children used in our present study, also developed a prediction model to estimate fat-free mass.30 However, the model was not based on readily available predictors as it relied on resistance from bioimpedance analysis and was not corrected for model optimism, which may explain why the model equation produced a R2 value of 91.8% compared with the value of 81.0% obtained in the present study.

Strengths and limitations of this study

The current investigation had several strengths in its approach to validating the developed UK based prediction model. Crucially, from each of the 19 countries, body fatness assessments were made using the same reference standard deuterium dilution method on which the UK based model was based,6 which provides accurate, safe, and minimally invasive measurements of total body water (and fat-free mass) with low error.13 14 Most studies included in this external validation were conducted recently and were sufficiently large to provide accurate estimates of the country specific prediction performance statistics. The pooled data used for this external validation across the 19 settings spanned a wide age range of participants aged 4-15 years, allowing us to obtain an accurate picture of the model performance across childhood and adolescence in the new settings. The maintained high predictive performance of the model at both the lower and the upper ends of the distribution of fat-free mass indicates the model’s potential utility for population based obesity surveillance (for example, in the English National Child Measurement Programme and the WHO Childhood Obesity Surveillance Initiative). The populations included about equal numbers of both high (56%) and low to middle income countries, which allowed for accurate subgroup assessment by income classification.

The study also had some limitations. Firstly, global representation was limited, with only a small number of participants included from East Asia and none from the Middle East. Secondly, five countries had fewer than 100 participants, which impacted the representativeness of the results and the precision of estimates obtained from these populations, although predictive performance statistics from these populations were consistent with those of the larger countries. Finally, deuterium dilution assessment involves estimating total body water, which is then converted into an estimate of fat-free mass using a chosen hydration constant.46 The hydration constants used across the individual studies were those originally applied by individual study authors. The study results were not, however, materially affected (results not presented) when using a consistent hydration constant46 for all studies, and therefore the choice of hydration constants is unlikely to have affected the results appreciably.

Implications for clinicians and policy makers

Although BMI is widely used because of its simplicity and reliance solely on measures of height and weight, it has well recognised serious limitations as a marker of body fatness in children.2 3 4 For example, BMI is unable to discriminate between fat mass and fat-free mass, and it has been shown that even at a given BMI among children of the same age and sex, both fat mass and fat-free mass can vary substantially,3 which is particularly concerning in light of evidence that, independent of height, fat mass in childhood is strongly associated with emerging cardiometabolic risk47 48 49 50 51 52 53 54 55 56 and is more strongly related with risk of type 2 diabetes in adulthood than overall weight (on which BMI is directly based).5 Furthermore, it has been suggested that fat-free mass, independent of fat mass, also has implications on adverse health conditions. This emphasises the needed for a shift away from proxy weight-for-height indices such as BMI, which produce inaccurate body fatness assessment in children12 57 58 59 and result in a large proportion being misdiagnosed with overweight or obesity, and towards more direct and accurate assessment of fat mass. The availability of the extensively validated prediction model provides a major advancement within this area of body fatness assessment in children. The accuracy and simplicity of the model, relying solely on readily available non-invasive measurements to assess fat-free mass and thus fat mass (fat mass=weight–exponential[predicted lnFFM]), has implications for its wider applicability both in routine healthcare practice and in population-wide obesity surveillance, monitoring, and prevention initiatives where more complex measurements of body fatness (such as waist circumference and skinfold thickness) are not so readily available. The consistency of the model performance across settings also strengthens the conclusions that the model, particularly after recalibration at local level, minimises the bias in fat-free mass predictions across a wide range of settings. However, the UK based model before local country specific recalibration of the intercept terms was shown to have good predictive ability across the settings, both in high and in low-middle income populations, and thus can be implemented in childhood settings where a recalibrated equation is not provided.

Body fatness markers require standardisation for height to minimise their correlation with height,60 to provide a consistent measure across age and sex, allowing for efficient monitoring and tracking of body fatness in childhood. Two common approaches to provide appropriate standardisation of fat mass for height are to convert fat mass to fat mass percentage (fat mass/weight×100) or to fat mass index (fat mass/heightp, where p is the power of height needed to obtain maximum height independence in the population of interest). Fat mass assessment (using either the updated country specific model equation provided when available or the original UK based model), after height standardisation (either as fat mass percentage or as fat mass index), can then be used in conjunction with respective established reference curves61 62 63 for improved surveillance, management, and prevention of obesity in childhood. A MS Excel calculator has been developed (see supplementary file) to allow for simple calculation of fat-free mass, fat mass, and fat mass percentage from the relevant predictor variables. Assessments of fat mass can also be made readily available to clinicians by embedding the validated equation within existing computer software used by general practitioners and paediatricians. This approach would be consistent with the use of other prediction algorithms in clinical practice, such as the QRISK3 or Framingham risk score (cardiovascular disease).64 65 It would also be possible and straightforward to apply the algorithms within existing obesity surveillance initiatives for children such as the English National Child Measurement Programme and the WHO Childhood Obesity Surveillance Initiative, to provide assessments of fat mass, fat-free mass, and fat mass index or fat mass percentage.

Further research

Further external validation of the model in countries or regions not included within this study would be of value. Additionally, the development of sex and age specific fat mass reference values, based on prospectively associated risks of diseases associated with obesity, could allow individuals to be classified into groups based on future disease risk attributable to their current fat mass levels, as opposed to current centile based approaches to classify fat mass.61

Improvements to the assessment of body fatness in children, currently based on body mass index (BMI), are required

Assessment of childhood fat mass, which is more strongly related with risk of type 2 diabetes in adulthood than weight (on which BMI is based), could provide improvements

A prediction model that accurately estimates fat mass levels in healthy children and adolescents has been developed and validated for the UK population, but its performance in other populations is unknown

This external validation study found strong predictive performance of the UK based model at estimating fat-free mass in a wide range of non-UK settings

The equation, which is based on readily available markers of height, weight, age, sex, and ethnic group, performed consistently well in both low-middle and high income settings, showing its wider generalisability

The recalibrated model equations for each of the 19 countries further improve the accuracy of fat-free mass predictions and are recommended for future use